Public Insurance:
Private Insurance:
Examples of “managed competition” in health insurance include:
Those with higher expected health care needs self-select into more generous insurance coverage
In MA, almost all markets are dominated (\(\geq\) 95% market share) by no more than 3 insurers. Why?
Basic structure:
Putting profit function in terms of risk units, the plan’s problem is:
\[\max_{p_{j}} \left(p_{j} + B - c_{j} \right) Q_{j}(p_{j}, p_{-j}),\]
where \(p_{j}\) is the plan’s price, \(c_{j}\) is their cost per enrollee, and \(Q_{j}\) is plan j’s quantity (in risk units)
\[\begin{align} \frac{d \pi}{d p_{j}} = Q_{j}(p_{j}, p_{-j}) + \frac{d Q_{j}}{d p_{j}} ( p_{j} + B - c_{j}) &= 0 \\ p_{j} + B - c_{j} = \frac{ - Q_{j} }{ \frac{d Q_{j}}{d p_{j}}} &= \left(\frac{d \ln Q_{j}}{d p_{j}}\right)^{-1} \\ p_{j} &= c_{j} - B + \left(\frac{d \ln Q_{j}}{d p_{j}}\right)^{-1} \\ b_{j} &= c_{j} + \left(\frac{d \ln Q_{j}}{d p_{j}}\right)^{-1} \\ \end{align}\]
Curto et al. (2021) study this in great detail…some key findings: